The couple have opened their home to the dog ahead of William's deployment to the Falkland Islands as an RAF search and rescue helicopter co-pilot this month.
It is thought William and Kate's new pet will live with them at their north Wales home, near an RAF base in Anglesey where the Duke has been working for more than a year.
A St James's Palace spokeswoman said: "The Duke and Duchess of Cambridge have a male cocker spaniel.
"It's from a litter known to the couple through a family connection. It's a few months old."
The Telegraph reported on its website that the dog's father is a pet that belongs to Kate's mother Carole Middleton.
The Falklands have been the subject of a diplomatic war of words between the British and Argentine Governments in recent months.
David Cameron and Argentine president Cristina Fernandez have previously accused each other of "colonial" behaviour.
In the latest salvo, Argentina's foreign ministry said William would be wearing the uniform of a "conqueror" when he arrives in the Falklands.
It also emerged on Tuesday that one of the Royal Navy's most advanced new warships - HMS Dauntless, a Type 45 destroyer - is being sent to the islands. But Ministry of Defence officials said the deployment was long planned and not a riposte to increased tensions over the sovereignty of the Falklands.
